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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2023, Volume 16, Issue 4, Pages 84–92
DOI: https://doi.org/10.14529/mmp230406
(Mi vyuru703)
 

This article is cited in 1 scientific paper (total in 1 paper)

Short Notes

An analysis of the Wentzell stochastic system of the equations of moisture filtration in a ball and on its boundary

N. S. Goncharov, G. A. Sviridyuk

South Ural State University, Chelyabinsk, Russian Federation
Full-text PDF (208 kB) Citations (1)
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Abstract: The deterministic and stochastic Wentzell systems of Barenblatt–Zheltov–Kochina equations describing moisture filtration in a three-dimensional ball and on its boundary are studied for the first time. In the deterministic case, the unambiguous solvability of the initial problem for the Wentzell system in a specifically constructed Hilbert space is established. In the stochastic case, the Nelson–Glicklich derivative is used and a stochastic solution is constructed, which allows us to predict quantitative changes in the geochemical regime of groundwater under pressureless filtration. For the filtration system under study, the non-classical Wentzell condition was considered, since it is represented by an equation with the Laplace–Beltrami operator defined on the boundary of the domain, understood as a smooth compact Riemannian manifold without an edge, and the external influence is represented by the normal derivative of the function defined in the domain.
Keywords: Wentzell system, Barenblatt–Zheltov–Kochina equation, Nelson–Glicklich derivative.
Funding agency Grant number
Russian Science Foundation 23-21-10056
Received: 03.08.2023
Document Type: Article
UDC: 517.9
MSC: 93E10
Language: Russian
Citation: N. S. Goncharov, G. A. Sviridyuk, “An analysis of the Wentzell stochastic system of the equations of moisture filtration in a ball and on its boundary”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 16:4 (2023), 84–92
Citation in format AMSBIB
\Bibitem{GonSvi23}
\by N.~S.~Goncharov, G.~A.~Sviridyuk
\paper An analysis of the Wentzell stochastic system of the equations of moisture filtration in a ball and on its boundary
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2023
\vol 16
\issue 4
\pages 84--92
\mathnet{http://mi.mathnet.ru/vyuru703}
\crossref{https://doi.org/10.14529/mmp230406}
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  • This publication is cited in the following 1 articles:
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